## Linear Operators: Spectral theory |

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Page 990

A bounded measurable function q on R is in the Ly - closed linear subspace of Lo

( R ) which is

. Conversely , if o is in the Li - closed linear manifold

A bounded measurable function q on R is in the Ly - closed linear subspace of Lo

( R ) which is

**determined**by the characters in any neighborhood of its spectral set. Conversely , if o is in the Li - closed linear manifold

**determined**by the ...Page 1321

The matrices I = ( y ) and I " = ( yi ) in the preceding theorem are uniquely

PROOF . We have seen in the derivation of Theorem 8 that the functions az ( t )

and Bi ( t ) ...

The matrices I = ( y ) and I " = ( yi ) in the preceding theorem are uniquely

**determined**by the jump equations and by the boundary conditions defining T.PROOF . We have seen in the derivation of Theorem 8 that the functions az ( t )

and Bi ( t ) ...

Page 1323

To

numbers ai ( t ) and Bi ( t ) we have the n ... By symmetry ( 11 ) and ( Vás ) are

also

( K ) = 0 ...

To

**determine**the u * + u * = ( p * + q * ) - ( u * + v * ) = ( n + k * ) - ( u * + v * )numbers ai ( t ) and Bi ( t ) we have the n ... By symmetry ( 11 ) and ( Vás ) are

also

**determined**uniquely by the jump conditions and the boundary conditions E ;( K ) = 0 ...

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